In this paper, a new deep-learning architecture for solving the non-linear
Falkner-Skan equation is proposed. Using Legendre and Chebyshev neural blocks,
this approach shows how orthogonal polynomials can be used in neural networks
to increase the approximation capability of artificial neural networks. In
addition, utilizing the mathematical properties of these functions, we overcome
the computational complexity of the backpropagation algorithm by using the
operational matrices of the derivative. The efficiency of the proposed method
is carried out by simulating various configurations of the Falkner-Skan
equation.

本文提出了一种新的深度学习架构来解决非线性 Falkner-Skan 方程，利用 Legendre 和 Chebyshev 神经模块展示了如何在神经网络中使用正交多项式以提高人工神经网络的逼近能力，并利用这些函数的数学性质，通过使用导数的运算矩阵克服了反向传播算法的计算复杂性，通过模拟 Falkner-Skan 方程的各种配置来验证了该方法的效率。